One thousand people, six degrees of separation

One thousand people

There are only one thousand people in the world – or so I say when joking about coincidental encounters.

How else can you explain that I constantly run into the same people in entirely different social circles? I keep meeting people who are friends with other friends I know from not just other parts of my life, but from entirely different countries. I regularly add people on LinkedIn, only to find that we have a mutual contact from an entirely distant past. These things just keep happening.

Clearly, I faux-theorized, the only explanation is that there can’t possibly be more than a thousand people in the world.

Since then, I’ve been clinging to this joke to the point where it should have stopped being funny long ago. But it didn’t die out – it just got bigger. My friends, being the scientifically minded geeks that they are, regularly feed my amusement by challenging my theory: “You must have seen TV footage of crowds of more than one thousand people!” “What about a situation where there are five or ten thousand people in a stadium and each one can see the others?” “How do you explain that you have more than a thousand Twitter followers?”

I’ve had fun making up the answers: “CGI.” “Advanced robotics and mind control.” “Fake accounts, obviously.”

Conspiracy theories

Many of my replies are existing conspiracy theories. The belief that images are Photoshopped or that video footage is created by advanced animation techniques is quite common on online message boards, where a lot of images really are manipulated to trick the viewer. The same communities are quite used to the practice of fake online profiles. Disbelief in TV footage dates back to at least 1969, when the Moon landing was broadcast – either from the actual Moon, or from a Hollywood stage, depending on who you believe. Even the idea that, unbeknowst to us, there are technologies advanced enough to recreate entirely convincing life-like robots, is very similar to a number of existing conspiracy theories that suggest that companies or governments are suppressing common access to particular technologies.

Mass mind control? That, too, is an existing conspiracy theory. It’s one of the sub-plots of the extremely convoluted New World Order conspiracy theory, which suggests that a small group of people is secretly ruling the entire world. One of the things they presumably do, is control our thoughts. The conspiracists apparently haven’t considered the obvious paradox that, if we are all subject to this kind of mind control, there is no way of knowing whether or not the truth or the conspiracy theory is the truth.

My favourite part of the New World Order conspiracy theory is that it also refers to something called the “myth of overpopulation”: Earth is not really overpopulated, they say. See, it fits my theory exactly if I want it to.

Six degrees

Even though I am endlessly entertained by the fact that my fake theory about coincidental encounters fits into the grand scheme of existing conspiracy theories, I obviously don’t really believe that there are only one thousand people in the world.

There is a much likelier and more scientific explanation for the fact that I keep running into the same people that is even more simple and more wonderful and amazing than any conspiracy theory put together: Small world networks, popularly known as “six degrees of separation”.

One of the most famous applications of the small world theory is the Kevin Bacon game. In 1994, stuck indoors during a snow storm, three students at Albright College in Pennsylvania passed the time by watching some movies. They noticed that the actor Kevin Bacon appeared in quite a lot of films. They started playing a game, where they would connect any given actor with Kevin Bacon through shared movie credits. When they found the connections, they tended to be quite short – often fewer than six steps.

Through online news groups and TV appearances, the game “Six Degrees of Kevin Bacon” gained a cult following among movie fans and students. You can play it online, on the Oracle of Bacon website, which cross-checks any actor with the Internet Movie Database (IMDb) and finds the shortest path to Kevin Bacon.

The name “Six Degrees of Kevin Bacon” refers to the popular idea that anyone in the world can be connected to anyone else by no more than six steps. This concept originates in a 1929 short story by Hungarian author Frigyes Karinthy, in which one of the characters suggests that anyone in the world can be contacted by anyone else using a chain of no more than five intermediate people who each know other. (In other words: in six steps.)

Testing the six degrees theory

Karinthy’s hypothetical idea was put to the test in the 1960s, when Yale Psychology professor Stanley Milgram carried out a key experiment using the US postal system. He selected a number of individuals in Omaha, Nebraska and Wichita, Kansas and asked them to try to contact a particular person in Boston using only a chain of acquaintances. They were to send the letter on to a person that they thought would be more likely to know the final person, and then that person did the same, until the end of the chain was reached. Not everyone participated, and many of the chains were broken, but of the ones that were completed, the average number of steps it took to reach the final person was less than six.

This experiment, while famous, is not the perfect proof for the “six degrees” phenomenon, and has received some criticism: Longer chains were more likely to be broken; people were not selected entirely at random; the number of broken chains was very high; and people often selected their recipients based on geography, even though they might have had a close-living acquaintance who personally knew the target.

A major breakthrough in the study of social connections came in 1998, a few years after the Six Degrees of Kevin Bacon game was popularized, when Duncan Watts and Steven Strogatz published a paper in Nature called “Collective Dynamics of ‘Small World’ Networks”. In this paper they showed that social networks – such as the network of movie actors in IMDB – can be mathematically simulated by something they called “small world” networks.

Small world or six degrees networks are characterized by the presence of hubs: objects in the network that connect to more other objects than most of the objects in the network do. Translated to social networks, it simply means that some people have more aquaintances than others do. When connecting one object with another within such a network, the shortest path towards six degrees often includes a hub.

Explaining social connections

This is why the Six Degrees of Kevin Bacon game works so well. Kevin Bacon is a hub. He has been in more movies than many other actors. The entire party game can be simulated mathematically. Watts and Strogatz show in their paper that the average path length between actors in the IMDb was about 3.65. That is an average distance between any pair of actors. The Oracle of Bacon Website actually calculates the average distance of any actor to Kevin Bacon number at less than that, which you would expect for a hub.

This is also why I keep seeing the same people everywhere. Mutual acquaintances that I share with others are often hubs: people who have many social connections. The small world network theory explains my observations much more elegantly than my one thousand people theory. Not only is it mathematically testable (you could use the LinkedIn or Facebook contacts of everyone I know and map out my whole social network), but it doesn’t require any additional subtheories.

Explaining much more than social connections

When my one thousand people fake theory was challenged by my friends, I could explain everything using various conspiracy theories that had little to do with the original theory. It would have required all of the individual theories to be true: not just my initial statement that there are only a thousand people in the world, but also the caveats that several of my Twitter followers are fake accounts, that all TV footage of gatherings of more than a thousand people is digitally altered, and that life-like robots are employed en masse to continually confuse us all.

The small world theory is not only a much better explanation for the connectedness of people, but it’s able to describe other phenomena as well.

Airport connections follow the same mathematical model as social networks do. They, too, have hubs. Chicago O’Hare and London Heathrow are some of the busiest airports in the world. Airport hubs make air travel more convenient, because it reduces the number of flight changes you need to make to get from A to B. It’s a nuisance, though, when a hub airport is shut down, because this now affects a large portion of global air travel.

Because both social interactions and airport connections fit the small world model of networks, mathematical modelling of such networks plays an important role in the prediction of the spread of epidemics. In addition, many networks within biological systems are also small world networks, such as neural connections in the brain or protein interaction networks within a cell.

Not only does the small world network model explain perfectly why I keep running into familiar people, but it explains much more on top of that, and it’s far more beautiful in its simplicity than my crazy fake one thousand people theory.

There are more than one thousand people in the world

Obviously, my one thousand people theory is just a silly joke, but some people really do believe in conspiracy theories or cling desperately to wrong explanations for observations in nature. A similarly convoluted system of one weak unscientific theory patched together with a bunch of excuses to make it fit any observations to the contrary has been seeping into classrooms – especially in parts of the United States – as an explanation for the origin of living things, despite the availability of a much more testable and scientifically valid explanation.

When Milgram did his six degrees postal experiment, it wasn’t perfect. It fit an idea, and he was on the right track, but it needed some more work. The paper by Watts and Strogatz was a huge step forward, but they, too, don’t get the final word. Network theory is constantly growing and building upon previous work, as are all scientific fields. Conspiracy theories and fake explanations can’t grow, but need to be patched up when they don’t work. They may make for exciting stories, and they can be fun to talk about, but in the end, they don’t do a very good job of explaining things.

And that is why I know very well that there are far more than one thousand people, even when it feels like a “small world” a lot of the time.

Eva Amsen is a writer, science communicator and blogger. She has been writing about science and scientists in art/culture/life since 2005, both on this blog and for other sites and publications.
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